Does this mean that if a Half-Orc, that is at 1 hit point, is hit by a giant spider taking >1 piercing damage, and the Half-Orc uses Relentless Endurance to remain at 1 hp, that they would still drop to 0 from the poison damage?

— Eric Green (@quadhund) August 8, 2018

That's correct.

— Jeremy Crawford (@JeremyECrawford) August 8, 2018